Write a quadratic polynomial, whose zeroes are $-4$ and $-5$.
Given: Zeroes of a polynomial are $-4$ and $-5$.
To do: To write the polynomial.
Solution:
As given zeroes of a polynomial are $-4$ and $-5$.
Sum of the zeroes$=-4+( -5)=-9$
Product of the roots $-4\times-5=20$
Thus, the polynomial is:
$p( x)=x^2-( sum\ of\ the\ zeroes)x+ ( product\ of\ the\ zeroes)$
$\Rightarrow p( x)=x^2-( -9)x+20$
$\Rightarrow p( x)=x^2+9x+20$
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